Bad Questions

I don’t often agree with Jay Mathews.

Mathews was the long time education reporter for the Washington Post and now writes a weekly column for the paper. I’ve written many posts about his adoration of KIPP charter schools, the unrequited love of the Advanced Placement program, and especially his Challenge Index, his annual ranking of high schools based solely on the number of AP tests taken by students.

However, his post from last week, which is not really about education, is one I can get behind. In it, he highlights two popular questions used by polling companies that produce little to no useful information, calling them dumb and deserving of ridicule.

One comes from the annual poll done by Gallup for Phi Delta Kappa, a professional association for educators. It asks people “What grade would you give your local public schools, the nation’s public schools and, if you have children at home, their schools?” The results are pretty much the same every year.

Since 1985, the results have been consistent. Respondents award their children’s specific schools the highest grades, with about three-quarters giving A’s and B’s. About half of them give their local schools A’s and B’s. About a fifth give A’s and B’s to the nation’s public schools.

My kid’s school is great. But those other schools, and the national education system, are crap. Of course PDK asks other questions about many aspects of education (in 2015, 64% of respondents said there was too much emphasis on standardized testing) but it’s that top number that is most widely reported by the headline driven media. And it’s too often used to perpetuate the “failing public schools” narrative. If people tell a survey taker something, it must be true.

The other poll question Mathews ridicules is even worse.

The right-track-wrong-track question is even more aggravating because it is so often extolled as a mark of voters’ desires. The latest Washington Post-ABC News poll uses this question: “Do you think in this country things are generally going in the right direction or do you feel things have gotten pretty seriously off on the wrong track?”

Over the 44 years that polling companies have asked that question “results have been on the negative side nearly 90 percent of the time”. Again, the surveys include other related questions but it’s the right-track-wrong-track number that gets put into the headlines and analyzed by pundits who probably haven’t bothered to read any of the supporting data or metrics used to select the sample.

Both of these examples are why K12 math instruction needs to include a whole lot more statistics. Maybe if more people reading these headlines actually understood something about polling methodology they might push back and question both the results and the reporting of them. Some of those better informed graduates might even become presenters on those talking heads channels and bring those questions to their jobs.

School Math is the Wrong Subject

Conrad Wolfram, a mathematician and “director of what’s arguably the world’s ‘math company’” (that would be Wolfram Research), believes “today’s educational math is the wrong subject”. Meaning that what we present to students as “mathematics” is not anything like what it is in the real world.

In the real world we use computers for calculating, almost universally; in education we use people for calculating, almost universally.

This growing chasm is a key reason why math is so despised in education and yet so powerful and important in real life. We have confused rigor at hand-calculating with rigor for the wider problem-solving subject of math. We’ve confused the once-necessary hand mechanics of the past with the enduring essence of math.

At its heart, math is the world’s most successful system of problem-solving. The point is to take real things we want to work out and apply, or invent, math to get the answer. The process involves four steps: define the question, translate it to mathematical formulation, calculate or compute the answer in math-speak and then translate it back to answer your original question, verifying that it really does so.

Teachers and textbooks give lip service to math as a tool for problem-solving but do little to help students understand the process Wolfram describes. As a result, the work kids do in “math” class is dry, boring and largely useless. For the most part, students learn to step through algorithms that the real world turned over to computers and calculators many decades ago.

I love how he describes “word problems” (now often euphamistically called “applications”) “as toy problems and largely outside any context most students can relate to”.

But it’s not just about turning the computation part over to computers. Wolfram says we need to completely replace the current mathematics curriculum taught in most schools.

Instead of rote learning long-division procedures, let’s get students applying the power of calculus, picking holes in statistics, designing a traffic system or cracking secret codes. Such challenges train both creativity and conceptual understanding and have practical results. But they need computers to do most of the calculating — just like we do in the real world.

All of us who have taught math in K12 have heard one common question from our students: “when are we ever going to use this?”. The fact that the honest answer is “probably never” should be a clue that something needs to change.

Powerball Math

It has been sorta fun watching all the hype surrounding the billion dollar Powerball lottery. Lots of stories about what could be done with that much money (greatly reduced by taxes and other factors), with reporters and others trying to make sense of the odds of winning, too often comparing them to those of being struck by lightning.

[326/365] Lottery Money1However, the best piece in the flood of coverage came from Wired, explaining The Fascinating Math Behind Why You Won’t Win Powerball. Including how the non-profit organization behind Powerball recently changed the format to make it much harder to win the top prize, and easier to win the pocket change prizes.

As I’ve previously ranted about, this is the kind of math that should be at the foundation of our K12 school curriculum. Real world, interesting, practical,2 stimulating lots of questions with connections to other areas of study. Instead of sending every student through the school theoretical math tunnel heading straight for Calculus, a subject used by very few adults.

Performing Mathematics

It seems as if there have been a lot of critiques of how we teachmath in the past couple of months. And now the author of a new book that links success in learning math to the “mindset” concept3 weighs in for The Atlantic, explaining the Math-Class Paradox.

If you ask most students what they think their role is in math classrooms, they will tell you it is to get questions right. Students rarely think that they are in math classrooms to appreciate the beauty of mathematics, to ask deep questions, to explore the rich set of connections that make up the subject, or even to learn about the applicability of the subject; they think they are in math classrooms to perform.

Students from an early age realize that math is different from other subjects. In many schools across the U.S., math is less about learning than it is about answering questions and taking tests–performing.

This school view of math as performance comes from their teachers, especially in elementary school, who “boil the subject down to producing short answers to narrow questions under pressure”. Hoping, of course, that this approach will get the kids to produce on the all-important spring standardized tests.

However, you can’t really blame teachers. They are working with the math curriculum, pretty much the same one taught in K12 for a hundred years or more, they have been given.

The fact that a narrow and impoverished version of mathematics is taught in many school classrooms cannot be blamed on teachers. Teachers are usually given long lists of content to teach, with hundreds of topics and no time to go into depth on any ideas. When teachers are given these lists, they see a subject that has been stripped down to its bare parts–like a dismantled bike–a collection of nuts and bolts that students are meant to shine and polish all year. Such lists not only take away the connections that weave all through mathematics, but present math as though the connections do not even exist.

Those connections, not only within mathematics but the applications to many other disciplines, was what I found most interesting when I taught the subject. And I tried hard to convey those connections to my students. But even in the pre-NCLB era when the end-of-course exam did not loom as large, the curriculum was still overloaded with crap. Time for open-ended questioning and exploring the messy world of applied math was still limited.

Prioritizing on Irrelevance Has Real Consequences

Following up on my math rant from yesterday, an opinion piece from the Post’s Answer Sheet blog adds some thoughts to the idea that our traditional math curriculum, as well as how math is taught in most schools, needs a major overhaul.

Now, calculus sounds essential to pre-eminence in science and engineering. It sounds like a gateway to the enticing “jobs of the future.” But here’s the reality. Other than high-school calculus teachers, adults no longer perform the low-level mechanics (months studying various integration techniques) that comprise high-school calculus. The tiny number of adults who do use Calculus in their careers compute integrals and derivatives … with computers.  Online resources like Wolfram|Alpha handle these tasks instantly — everywhere except in our classrooms. When it comes to calculus, a strong case can be made that we should do less.

Calculus reflects our true dichotomy in education. In a very different world where all of us have ready access to content and computational resource, we can have kids study things whose importance has faded or disappeared, or we can re-think what’s essential. To be specific, kids who take Calculus, generally forego statistics – a discipline that’s essential for citizenship and immensely valuable for careers. Organizations don’t need employees who can do integrals by hand using trig identities, but they’d love to hire young adults who can analyze data. With over 50 percent of recent college graduates under- or flat-out unemployed, prioritizing on irrelevance has real consequences. [emphasis is mine]

That rational thinking comes from Ted Dintersmith, a venture capitalist who organized, funded and produced the well-received documentary “Most Likely to Succeed,” and co-authored a book titled “Most Likely to Succeed:  Preparing Our Kids for the Innovation Era” (one I need to add to my reading list).

I also loved his description of the place given to actual educators and students at last month’s White House Summit on Next Generation High Schools in which he participated.

After the big-footprint speakers departed from the summit, we heard from compelling teachers, students, school leaders, district superintendents, and non-profit heads. They brought vision and bold ideas to the White House, despite being allocated just 120 seconds to describe their life’s work. The irony of a rapid-fire sequence of “talk at you lectures” on the topic of re-imagined learning wasn’t lost on this crowd.

Read the whole post for more fresh thinking on math in American schools.